Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1732 and 1738 the smallest integer that is 1505108 that is divisible by both numbers.
Least Common Multiple (LCM) of 1732 and 1738 is 1505108.
LCM(1732,1738) = 1505108
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 1732 and 1738. First we will calculate the prime factors of 1732 and 1738.
Prime Factorization of 1732
2 | 1732 |
2 | 866 |
433 | 433 |
1 |
Prime factors of 1732 are 2,433. Prime factorization of 1732 in exponential form is:
1732 = 22×4331
Prime Factorization of 1738
2 | 1738 |
11 | 869 |
79 | 79 |
1 |
Prime factors of 1738 are 2, 11,79. Prime factorization of 1738 in exponential form is:
1738 = 21×111×791
Now multiplying the highest exponent prime factors to calculate the LCM of 1732 and 1738.
LCM(1732,1738) = 22×111×791×4331
LCM(1732,1738) = 1505108
Factors of 1732
List of positive integer factors of 1732 that divides 1732 without a remainder.
1, 2, 4, 433, 866, 1732
Factors of 1738
List of positive integer factors of 1738 that divides 1738 without a remainder.
1, 2, 11, 22, 79, 158, 869, 1738
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1732 and 1738, than apply into the LCM equation.
GCF(1732,1738) = 2
LCM(1732,1738) = ( 1732 × 1738) / 2
LCM(1732,1738) = 3010216 / 2
LCM(1732,1738) = 1505108
(i) The LCM of 1738 and 1732 is associative
LCM of 1732 and 1738 = LCM of 1738 and 1732
1. What is the LCM of 1732 and 1738?
Answer: LCM of 1732 and 1738 is 1505108.
2. What are the Factors of 1732?
Answer: Factors of 1732 are 1, 2, 4, 433, 866, 1732. There are 6 integers that are factors of 1732. The greatest factor of 1732 is 1732.
3. What are the Factors of 1738?
Answer: Factors of 1738 are 1, 2, 11, 22, 79, 158, 869, 1738. There are 8 integers that are factors of 1738. The greatest factor of 1738 is 1738.
4. How to Find the LCM of 1732 and 1738?
Answer:
Least Common Multiple of 1732 and 1738 = 1505108
Step 1: Find the prime factorization of 1732
1732 = 2 x 2 x 433
Step 2: Find the prime factorization of 1738
1738 = 2 x 11 x 79
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1505108 = 2 x 2 x 11 x 79 x 433
Step 4: Therefore, the least common multiple of 1732 and 1738 is 1505108.